Stephen Milne, Nick Grainger, Duncan Scott and James Guy set a new British record in the process, coming in at 7:01.68 ahead of Russia in second place and USA in third.
Callum Jarvis, who helped the team secure their place in the final in the morning heats, was also awarded gold.
Peaty heroics not enough as USA pip Britain to 4x100m medley relay gold
Speaking afterwards, Grainger said: "That was amazing. I can’t get enough of it. Standing on that podium was absolutely fantastic. Having a team like this is just brilliant,”
"When James [Guy] touched at that finish I almost took Duncan [Scott] out running in for the hug. I was having the time of my life. I can’t properly put it into words."
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Paying tribute to Jarvis, he added: "This is an amazing team to be a part of but it’s more than this quartet. This morning we saw Callum [Jarvis] put together an amazing swim which put us in a great lane tonight and ultimately put us on the top step of the podium.”
Guy has another opportunity for a medal on Saturday after making it to the Men's 100m Butterfly final, breaking the British record twice in one day, in the process.
Also on Friday, GB's Ross Murdoch fell just short of a medal in the Men's 200m Breaststroke, and Molly Renshaw finished sixth in the final of the Women's 200m Breaststroke.
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